Only the total number of interactions prior to escape matters in the processing of nuclei injected by the accelerator, so only the ratio of the interaction and escape times is relevant for fixing the composition and energy spectra of CRs emerging from the source environment, given the injected composition and spectrum. We denote these ratios for the reference nucleus by the model parameters \(r_\mathrm {esc} \equiv \tau _\mathrm {esc}^\mathrm {ref}/\tau _\mathrm {int}^\mathrm {ref} = \langle N_\mathrm {int}^\mathrm {ref} \rangle \) , the ratio of the escape and total interaction times, and \(r_{g\gamma } \equiv \tau _g^\mathrm {ref} / \tau _\gamma ^\mathrm {ref} = \langle N_\gamma ^\mathrm {ref} \rangle / \langle N_g^\mathrm {ref} \rangle \) , the ratio of the hadronic and photohadronic interaction times. In previous work [1]}, [2]}, the escape time was taken to be a power law in rigidity, \(R\equiv E/Z\) , so that \(\tau _{\rm esc} = \tau ^\mathrm {ref}_{\rm esc} (R/R_\mathrm {ref})^{\delta _{\rm esc}}\) , relative to the reference nucleus, with \(\delta _\mathrm {esc}\)  a free parameter of the model limited to be within \([-1,-1/3]\)  covering the expected range from Kolmogorov to Bohm diffusion. Here we adopt a more detailed parameterization (described in Section REF ) based on simulations of CR propagation in turbulent magnetic fields, e.g., [3]}: \(\tau _\mathrm {esc}(R) = \frac{L^2}{6D(R)} + \frac{L}{c}\) . This implies faster escape in the quasi-ballistic regime.
